1. The High-Density Symmetry Energy in Heavy Ion Collisions The High-Density Symmetry Energy in Heavy Ion Collisions Hermann Wolter Ludwig-Maximilians-Universität München (LMU) Massimo Di Toro, Maria Colonna, V. Greco, G. Ferini, (LNS Catania), Theodoros Gaitanos, (Giessen), Vaia Prassa, (Thessaloniki)

2. Schematic Phase Diagram of Strongly Interacting Matter Liquid-gas coexistence Quark-hadron coexistence Z/N 1 0 SIS18 neutron stars Supernovae IIa Isospin degree of freedom Outline: 1.Density and momentum dependence of the Symmetry Energy 2.Investigation via heavy ion collisions 3.Observables in the above-saturation density regime: difference flows, meson production ratios 4.Discussion of pion and kaon ratios SIS300

3. E sym pot (  ) often parametrized as Parametrizations around  0 : Equation-of-State and Symmetry Energy BW mass formula density- asymmetry dep. of nucl.matt.     stiff soft saturation point Fairly well fixed! Soft! EOS of symmetric nuclear matter symmetry energy asymmetry  density  Symmetry energy: neutron - symm matter, rather unknown, e.g. Skyrme-like param.,B.A.Li asy-stiff asy-soft neutron matter EOS

4. C. Fuchs, H.H. Wolter, EPJA 30 (2006) 5 The Nuclear Symmetry Energy (SE) in „realistic“ models The EOS of symmetric and pure neutron matter in different many-body aproaches SE ist also momentum dependent  p/n effective mass splitting  Lane potential Why is symmetry energy so uncertain?? ->In-medium  mass, and short range isovector tensor correlations (B.A. Li, PRC81 (2010));  use HIC to investigate in the laboratory and neutron star observations Rel, Brueckner Nonrel. Brueckner Variational Rel. Mean field Chiral perturb. SE nuclear matter neutron matter

5. E sym      MeV)     1230 Asy-stiff Asy-soft heavy ion collisions in the Fermi energy regime Isospin Transport properties, (Multi-)fragmentation (diffusion, fractionation, migration) Importance of Nuclear Symmetry Energy Constraints on the Slope of SE from Structure and low-energy HIC p, n rel. heavy ion collisions Isotopic ratios of flow, particle production Stringent constraint on many EoS models Neutron star mass-radius relation

6. 2-body collisions loss termgain term 1 11 1 2 34 non-relativistic: BUU Vlasov eq.; mean field EOS isoscalar and isovector isospin dependent, pp,nn,pn Remarks on Transport theories: Approximation to a much more complicated non-equilibrium quantum transport equation (Kadanoff-Baym) by neglecting finite width of particles (quasi-particle approximation) Relativistic equivalent available; RMF or EFT models for EOS: Consistency between EOS and in-medium cross sections: e.g. (Dirac) Brueckner approach Isovecor effects are small relative to isoscalar quantities; differences or ratios of observables to become independent of isoscalar uncertainties Collision term  dissipation, NO fluctuation term  Boltzmann-Langevin eq. Învestigation of the symmetry energy in heavy ion collisions  Transport theory

7. Very often the mean field and the cross sections are parametrized separately from each other. However, they should follow from the same theory for the self-energy. One of the best approaches to do this is Brückner theory (BHF or DBHF) In this approach both quantities are derived from the same in-medium T-matrix T T TT   VGGQTiVT Paui-blocking in the intermediate state Quasi-particle approximation (QPA)A(r,p) spectral function QPA - reduces no.of variables from 8 to 7  particle interpretation possible. - related to „off-shell transport“, perhaps important for subthreshold production

8. Heavy Ion Collisions at Relativistic Energies: “Flow“ Global momentum space Fourier analysis of momentum tensor : „flow“ v 2 : elliptic flowv 1 : directed flow Au+Au @ 400 AMeV, FOPI-LAND (Russotto, et al., PLB 697, 471 (11)) transverse flow (v1) not very sensitive, but elliptic flow (v2), originates in compressed zone determines a rather stiff symmetry energy, i.e.  =0.5  =1.5 neutron proton hydrogen ASYEOS experiment at GSI May 2011, being analyzed First measurement of isospin flow for 124 Sn “asymmetry”  = 0.2 neutron proton Asy-stiff Asy-soft U p/n [MeV]

9. What can one learn from different species? pions: production at all stages of the evolution via the  -resonace kaons (strange mesons with high mass): subthreshold production, probe of high density phase ratios of      and K 0 /K + :  probe for symmetry energy Particle Production Inelastic collisions: Production of particles and resonances: Coupled transport equations e.g. pion and kaon production; coupling of  and strange- ness channels. NN NKNK KK NN N  Elastic baryon-baryon coll.: NN  NN (in-med.  NN ), N  N ,  Inelastic baryon-baryon coll, (hard  -production): NN  N , NN  Inelastic baryon-meson coll. (soft  -production): N  Channels with strangeness (perturbative kaon production): Baryon-Baryon : BB  BYK (B=N,  ±,0,++, Y=  ±,0, K=K 0,+ ) Pion-Baryon :  B  YK (strangeness exchange) Kaon-Baryon : BK  BK (elastic, isospin exchange) No channels with antistrangeness (K - )

10. In-medium Klein-Gordon eq. for Kaon propagation: Two models for medium effects tested: Chiral perturbation (Kaplan, Nelson et al.) One-Boson Exchange (Schaffner-Bielich et al.) Scalar and vector isospin splitting Kaon potentials Splitting for K 0,+ (in OBE diff. for NL  and NL  In-medium K energy (k=0)

11. Au+Au@1AGeV G.Ferini et al.,PRL 97 (2006) 202301 Central density  and  multiplicity K 0,+ multiplicity stiff E sym soft E sym   Au+Au, 0.6AMeV time [fm/c]  and K: production in high density phase Pions: low and high density phase Sensitivity to asy- stiffness Dependence of ratios on asy-stiffness n/p   0,- /  +,++   - /  + Dynamics of particle production ( ,K) in heavy ion collisions  time [fm/c] NL  NL  NL

12. 1.„direct effects“: difference in proton and neutron (or light cluster) emission and momentum distribution 2.„secondary effects“: production of particles, isospin partners  -,+, K 0,+ NN NKNK KK NN N  in-medium inelastic   K and  potential (in- medium mass)  in-medium self-energies and width  potential, p, n Particle production as probe of symmetry energy Two limits: 1.isobar model (yield determined by CG-Coeff of  ->N  2.chemical equilibrium ->  - /  + should be good probe! box calculation Ferini et al., B.A.Li et al., PRL102  Therefore consider ratios  - /  + ; K 0 /K +

13. G.Ferini et al.,PRL 97 (2006) 202301 1. Mean field effect: U sym more repulsive for neutrons, and more for asystiff  pre-equilibrium emission of neutron, reduction of asymmetry of residue 2. Threshold effect, in medium effective masses: Canonical momenta have to be conserved. To convert to kinetic momenta, the self energies enter In inelastic collisions, like nn->p  -, the self-energies may change. Simple assumption about self energies of  Yield of particles depends on Detailed analysis gives Particle production as probe of symmetry energy (2) Two effects: Competing effects! - How taken into account in different calculations? -  dynamics may be too simple.

14. energy spectra Transport calculations reproduce the main features of pion production. But pion productin can also be used as a probe for the symmetry energy…. yields Pion production ( Pion production (Reisdorf et a., (FOPI), NPA 781, 459 (07))

15. MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09) MDI, x=1, very soft NL , stiff Ferini, Gaitanos,.. NPA 762 (05) NL  linear  =2, stiff Feng,… PLB 683 (10) SIII, very soft small dep. on SE J. Hong, P.Danielewicz APCTP workshop FOPI, exp  NPA 781, 459 (07))  Pion ratios in comparison to FOPI data Contradictory results of different calculations; Au+Au, semi-central

16. MDI, x=0, mod. soft Xiao,.. B.A.Li, PRL 102 (09) MDI, x=1, very soft NL , stiff Ferini, Gaitanos,.. NPA 762 (05) NL  linear  =2, stiff Feng,… PLB 683 (10) SIII, very soft small dep. on SE J. Hong, P.Danielewicz APCTP workshop FOPI, exp  NPA 781, 459 (07))  Pion ratios in comparison to FOPI data Contradictory results of different calculations; Au+Au, semi-central Possible causes: - Pion are created via  ‘s.  dynamics in medium (potential, width, etc) largely unknown. - Threshold and mean field effects - Pion potential: U  =0 in most calculations. OK? - differences in simulations, esp. collision term - Urgent problem to solve!!!

17. Kaon production as a probe for the EOS Subthreshold, Eth=1.58 MeV NN NKNK KK NN N  Two-step process dominant In havier systems. Collective effect M(K+) ~ (A part )    >1: evidence of two-step process Important to fix the EOS of symm. nucl. matter Fuchs, et al., PRL 86 (01)

18. IQMD K +, K 0 data from KaoS, FOPI and HADES and interpretation Au+Au, 1.5 AMeV Ni+Ni, 1.93 A MeV C. Hartnack, et al., Phys. Rep. 510 (2012) 119 Ar+KCl, 1.75 A MeV C. Fuchs, PPNP 56 (2006) 1 Rapidity distribution, Ni+Ni, 1.93 A MeV w/o pot with pot

19. Strangeness ratio : Infinite Nuclear Matter vs. HIC  Au ≈0.2 Au+Au@1AGeV (HIC)  Au ≈1.5 NL→ DDF→NLρ→NLρδ increas. asy-stiffness more neutron escape and more n→p transformation (less asymmetry in the source ) Density & asymmetry of the K-source Inf. NM G. Ferini, et al., NPA762(2005) 147 Pre-equilibrium emission (mainly of neutrons) reduces asymmetry of source for kaon production  reduces sensitivity relative to equilibrium (box) calculation

20. G.Ferini et al.,PRL 97 (2006) 202301 132Sn+124Sn Au+Au, 1 AGeV, central Inclusive multiplicities 132Sn+124Sn Nuclear matter (box calculation) - Stiffer asy-EOS  larger ratio! Opposite to mean field effect! - Kaons somewhat more sensitive than pions. esp. at low energies, close to threshold - Sensitivity reduced in finite nuclei due to evolution of asymmetry in collision Kaon production in HIC more asy-stiffness ChPT w/o pot Dependence of ratios on  eff and kaon potentials  robust relative to K-potential,  but dependent on isospin-dep part

21. Kaon ratios: comparison with experiment G. Ferini, et al., NPA762(2005) 147 and PRL 97 (2006) 202301 Data (Fopi) X. Lopez, et al. (FOPI), PRC 75 (2007) Comparision to FOPI data (Ru+Ru)/(Zr+Zr) equilibrium (box) calculations finite nucleus calculations sensitivity reduced in collisions of finite nuclei single ratios more sensitive enhanced in larger systems

22.  +/  - ratio B.A. Li, et al.  +/  - ratio, Feng, et al. Fermi Energy HIC, various observabl es, compilatio n MSU Present constraints on the symmetry energy Moving towards a determination of the symmetry energy in HIC but at higher density non-consistent results of simulations for pion observables. Au+Au, elliptic flow, FOPI Limits on the EOS in  -equilibrium, Including constraints from neutron stars and microscopic calc. A. Steiner, J. Lattimer, E.F.Brown, arXiv 1205.6871 Combined methods move towards stronger constraints

23. Summary and Outlook EOS of symmetric NM now fairly well determined, but density (and momentum) dependence of Symmetry Energy still rather uncertain, but important for exotic nuclei, neutron stars and supernovae. Constraints from HIC at sub-saturation (Fermi energy regime) and supra-saturation densities (relativistic collisions), and increasingly from neutron star observables. At subsaturation densities the constraints become more stringent (  ~1, L~60 MeV), but constraints are largely lacking at supra-saturation densities. Observables for the suprasaturation symmetry energy N/Z of pre-equilibrium light clusters (MSU, FOPI), difference flows, (first hints -> ASYEOS) part. production rations  - /  +, K 0 /K + (FOPI, HADES) More work to do in exp. (more data) and theory (consistency of transport codes,  dynamics) many knotty problems! An interesting field that connects nuclear structure, reactions and astrophysics Thank you Trento, Duomo